Atomic self-interaction correction for molecules and solids

TL;DR

This paper introduces an atomic orbital based approximate self-interaction correction scheme for density functional theory, improving the accuracy of ionization potentials, affinities, and bandgaps for molecules and solids.

Contribution

It develops a non-variational, localized atomic orbital method for SIC applicable to molecules and solids, linking it to LDA+U and demonstrating its effectiveness.

Findings

Kohn-Sham HOMO eigenvalues approximate experimental ionization potentials.

HOMO eigenvalues of negatively charged molecules match molecular affinities.

Re-scaling is needed to accurately reproduce insulator bandgaps.

Abstract

We present an atomic orbital based approximate scheme for self-interaction correction (SIC) to the local density approximation of density functional theory. The method, based on the idea of Filippetti and Spaldin [Phys. Rev. B 67, 125109 (2003)], is implemented in a code using localized numerical atomic orbital basis sets and is now suitable for both molecules and extended solids. After deriving the fundamental equations as a non-variational approximation of the self-consistent SIC theory, we present results for a wide range of molecules and insulators. In particular, we investigate the effect of re-scaling the self-interaction correction and we establish a link with the existing atomic-like corrective scheme LDA+U. We find that when no re-scaling is applied, i.e. when we consider the entire atomic correction, the Kohn-Sham HOMO eigenvalue is a rather good approximation to the experimental ionization potential for molecules. Similarly the HOMO eigenvalues of negatively charged molecules reproduce closely the molecular affinities. In contrast a re-scaling of about 50% is necessary to reproduce insulator bandgaps in solids, which otherwise are largely overestimated. The method therefore represents a Kohn-Sham based single-particle theory and offers good prospects for applications where the actual position of the Kohn-Sham eigenvalues is important, such as quantum transport.